5) When calculating L{f(t)} huhere f(t) is the function whose graph is shown in the attached figure, we obtain : 12e a) 12e b) 12e™*

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: 3. Show that the functionf on [-1,1] defined as if f (r) = 1+e if x = 0 is discontinuous at x = = 0.…

A:

Q: 3. Compute the value of F.dr if F = -yi + xj and C is a semicircle from (-1,1) to (1,-1).

A:

Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

Q: 5. Show that the function h(r, y) defined by if + y 1 is discontinuous.

A:

Q: 10.Sketch graph of the following multivariable functions a. z = +1 b. + c. z² = x² ++1 y2

A:

Q: 6. Consider the function f Cx)=5(o+5)-25 if X#し if xfO D.IS fCx) continuous at X-0? EXPlain

A:

Q: ,15 15 ** Let f be a continuous function. If f(x)dx = 15 and f(x)dx = -8, then f(x)dx equals -5 В C…

A:

Q: What are the local minimum and maximum values of f. If an answer does not exist, use DNE.)

A: Consider f'(x) = 0.

Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 4e* on the interval [0,…

A:

Q: (1 point) Suppose f" (x) = –16 sin(4æ) and f' (0) = –4, and f(0) = -1. -1. f(T/2) :

A: Given,f''x = -16sin4xIntegrating on both side with respect to x, we get;f'x = - 64cos4x +…

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

A:

Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

A:

Q: 3.Show, by means of the example f(t) = sin t, that f ∗ f is not necessarily nonnegative.

A:

Q: (5) Find the most general function f(t) so that the curve F(t) =, shall lie in a plane.

A: The most general function for f(t) is a constant function, f(t) = c:   <a cost, a sint, c>

Q: 1. Suppose f is a function which satisfies f(x + y) = f(x) + f (y) for all x,y e R. What is the…

A: Let f is a function which satisfies f(x+y) = f(x) + f(y)  for all x,y∈R   f(x+y) = f(x) + f(y) ,   ∀…

Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: The triangle inequality is the most common algebraic tool for rigorously proving order…

A: Note:- As you want the answer of 4th statement so i am solving only it.

Q: Use the given graph of f(x) = /x to find a number 8 such that if Ix - 4| < 8 then Vx - 2 < 0.4 yA…

A: use limit definition for evaluating the value  of delta.

Q: 2. Find a function of the form y = Asin(x) + D or y = Acos(x) +D whose graph matches the graph…

A: We know that time period of sin(x) and cos(x) both are 2π

Q: Find a point e satisfying the conclusion of the MVT for the function y(x) = 2e* on the interval [0,…

A:

Q: 1. Find the discontinuity point/s of f(x) =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: +1 Differentiate the function f (x) = In +1

A:

Q: 1) Sketch the graph of a function with the following conditions: V D = {x € R\x # 0,4, 5} f(x) 0…

A: We have condition at function.D = {x∈R|x≠0,4,5}f(x)&lt;0, When x∈(-2,0)∪(2,4)f(x)&gt;0, When…

Q: Determine {f],where the periodic function is described by its graph. 19 2a 3a 40 (1-as) (1-) 1.…

A:

Q: lim 3i 4 +

A:

Q: 2. Use the given graph of f(x) = x² to find a number 8 such that if 0 < ]x – 1| < 8. then. [x² – 1|…

A:

Q: Assume that f is a function with domain [0,1] that is differentiable in (0,1). Assuming that f (0) =…

A:

Q: Find number k, so that f is continuous at every point. tan kx f(x) = x 4x+3 k2, x 20 O O and= Cannot…

A: The function is given by fx = tankxx ,x&lt;04x+3k2 ,x≥0 To evaluate : The value of k so that f is…

Q: 11. Prove from the definition that the following functions are differentiable. ()- (b) f =xy?

A: By the definition, the function f(x,y)=xy^2 is differentiable if fx(x,y) and fy(x,y) both exist.

Q: 5. Let f(x)= x . arccos x. Find f'(-/3/2) ||

A:

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

Q: 35. Given that f(z) is a continuous even function, then A 0 D

A: We will use the definition of an even function and properties of definite integrals to find the…

Q: 6. Prove if the following function is differentiable y2 = (arctanx + 1)°*

A:

Q: Suppose that f is a differentiable function with f(2) = 5 and f'(2) = 7. Let h(x) = f(e*). Find an…

A: Find the derivative for the function h(x). Now, the derivative for the function is the slope for the…

Q: 5 Show that the function h(r, y) defined by if r +y? < 1 h(x, y) 0; if r +y 2 1 is discontinuous.

A: For continuity of 2 variable function L.H.L=R.H.L=Function value at (x,y). limx→a+,y→b+…

Q: 10. Consider the function if a E Q -a? if x ¢ Q. f(x) = Prove that f'(0) = 0. %3D

A: Solution:Given  f(x)=x2if x∈Q-x2if x∉QTo prove f'(0)=0Formuladdx(xn)=nxn-1

Q: 2. Let f(x) = eª + 4e* 1 for x E [0, 3]. Determine the length of the graph of f.

A:

Q: 7.14. Show that if f = u+iv is analytic in a region S and u is a constant function (i.e.,…

A: Analytic function which is a constant

Q: Consider an F-curve with d f = (2, 14). Identify the degrees of freedom for the numerator.

A: The degrees of freedom for the F-statistic is df=(k−1, n−k).

Q: Consider the relation x2z2 = arctan (xyz) + 4, which defines z as an implicit function of x and y,…

A:

Q: Suppose h(x) = [,f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) -4-…

A:

Q: Develop the Simpson's 1/3 rule to evaluate the value of a function. f(x) 1 between the yalue 1 and 5…

A: Hey, since there are multiple subpart posted, we will answer first question. If you want any…

Q: Sketch a graph of the function f(x) = – 2 sin (x + 4) +: + 1. 5+ 4 3- -37/2 -5/4 -3/4 -T/2 -TU4 3714…

A:

Q: 5. Consider the function S 2r – 1, si x < 2 f(x) = 6-x, si x 2 2. The Limit x 2 f(x) is:

A:

Q: Find a point e satisfying the conclusion of the MVT for the following function and interval: f(x) =…

A:

Q: 5.6 Differentiate f with respect to t and g with respect to X, where

A: Let us start solving step by step....differentiate with respect to t and g with respect to x

Q: Suppose that a function f(x, y) satisfies fxx fyy – (fxy)² > 0 at a point (a, b). How is the sign of…

A: